From random walk to multifractal random walk in zooplankton swimming behavior

From random walk to multifractal random walk in zooplankton swimming behavior. Zoological Studies 43(2): 498-510. Herein, we investigate the statistical properties of the swimming behavior of two of the most common freshwater and marine zooplankters, the cladoceran, Daphnia pulex, and the copepod, Temora longicornis. Both species undergo a very structured type of trajectory, with successive moves displaying intermittent ampli-tudes. We present an original statistical procedure, derived from the fields of turbulence and anomalous diffu-sion and specifically devoted to the characterization of intermittent patterns. We then show that the swimming paths belong to“multifractal random walks”, characterized by a nonlinear moment scaling function for distance versus time. This clearly differs from the traditional Brownian and fractional Brownian walks expected or previ-ously detected in animal behaviors. More specifically, we have identified differential behaviors in the horizontal and vertical planes. This suggests the existence of reminiscence of diel vertical migration as a predator-avoid-ance strategy or differential swimming behaviors related to mating, feeding, or predator-avoidance strategies. We also compare the structure of the swimming paths to the multifractal behavior of microscale phytoplankton distributions demonstrated in turbulent environments, and briefly discuss the potential causes of the observe